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log(x + y) = 2xy: find y'(0)

The same question, asked 5 times: 10 May 2023 S1, 10 May 2023 S2, 9 May 2024 S2, 10 May 2024 S2, 12 May 2024 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2023 S1

    136
    If y is a function of x and log⁡(x+y)=2xy\log(x+y)=2xy, then the value of y′(0)y'(0) is

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  2. Question 2

    10 May 2023 S2

    104
    If y is a function of x and log⁡(x+y)=2xy\log(x+y) = 2xy, then the value of y′(0)y'(0) is

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  3. Question 3

    9 May 2024 S2

    126
    If yy is a function of xx and log⁡(x+y)=2xy\log(x+y) = 2xy, then the value of y′(0)y'(0) is

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  4. Question 4

    10 May 2024 S2

    129
    If yy is a function of xx and log⁡(x+y)=2xy\log(x+y)=2xy, then dydx\dfrac{dy}{dx} at x=0x=0 is

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  5. Question 5

    12 May 2024 S1

    133
    If log⁡(x+y)=2xy\log(x+y)=2xy, then dydx\frac{dy}{dx} at x=0x=0 is

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